A VECTOR-HOST EPIDEMIC MODEL WITH HOST MIGRATION

The host migration is one of the important elements that cause the worldwide diffusion and outbreak of many vector-host diseases. In this paper, we formulate a patchy model to investigate the effect of host migration between two patches on the spread of a vector-host disease. The results of the paper show that the reproduction number R-0 is a threshold value that determines the uniform persistence and extinction of the disease. If the reproduction number R-0 < 1 the disease free equilibrium (DFE) is locally asymptotically stable. If the reproduction number R-0 > 1 then the DFE is unstable and the system is uniformly persistent. It is also shown that a unique endemic equilibrium, which exists when R-0 > 1, is locally stable if both regions are identical.